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Monday, July 22, 2019

Given the successes of energy-based
formalisms in physics, it is natural to want to extend them into other domains
like computation and cognition.

In this vein: My aim here is to sketch what I
think is a workable approach to an energetics of computational processes
(construed very broadly).

By this I mean: I will explain how one can
articulate highly general principles of the dynamics of computational
processes, that take a similar form to physics principles such as the
stationary action principle (which often takes the form of "least
action") and the Second Law of Thermodynamics (the principle of entropy
non-decrease).

Why am I interested in this topic?Two related reasons, actually.

First, I would like to create a "General
Theory of General Intelligence" -- or to be more precise, a general theory
of what kinds of systems can display what levels of general intelligence in
what environments given realistically limited (space, time and energy)
resources.Marcus Hutter's Universal AI
theory is great but it doesn't say much about general intelligence under
realistic resource assumptions, most of its power is limited to the case of AI
systems with unrealisticallymassive
processing power.I have published some ideas on this before --
e.g. formalizing Cognitive Synergy in terms of category theory,
and articulating the Embodied Communication
Prior in regard to which human-like agents attempt to be intelligent
-- but nothing remotely near fully satisfying.So I'm searching for new directions.

Second, I would like to come up with a real
scientific theory of psi phenomena.I am
inclined toward what I call "euryphysical" theories -- i.e. theories
that involve embedding our 4D spacetime continuum in a larger space (which
could be a higher dimensional space or could be a non-dimensional topological
space of some sort).However, this begs
the question of what this large space is like -- what rules govern
"dynamics" in this space?In my paper on Euryphysics, I
give some rough ideas in this direction, but again nothing fully satisfying.

It would be nice if mind dynamics -- both in
a traditional AI setting and in a more out-there euryphysical setting -- could
be modeled on dynamical theories in physics, which are based on ideas like
stationary action.After all, if as
Peirce said "matter is just mind hide-bound with habit" then perhaps
the laws of matter are in some way simplifications or specializations of the
laws of mind -- andmaybe there are laws
of mind with roughly analogous form to some of the current laws of physics.

A Few Comments on Friston's Free Energy Ideas

Friston's "free energy principle"
represents one well-known effort in the direction of modeling cognition using
physics-ish principles.It seems to me
that Friston's ideas have some fundamental shortcomings -- but reviewing these
shortcomings has some value for understanding how to take a more workable
approach.

I should clarify that my own thinking
described in this blog post was not inspired by Friston's thinking to any
degree, but more so by long-ago reading in the systems-theory literature --
i.e. reading stuff like Ilya Prigogine's Order
out of Chaos] and Eric Jantsch's The
Self-Organizing Universeand Hermann
Haken's Synergetics.These authors represented a tradition
within the complex-systems research community, of using far-from-equilibrium
thermodynamics as a guide for thinking about life, the universe and
everything.

Friston's "free energy principle"
seems to have a somewhat similar conceptual orientation, but confusingly to me,
doesn't seem to incorporate the lessons of far-from-equilibrium thermodynamics
that thoroughly, being based more on equilibrium-thermodynamics-ish ideas.

As the latter post notes, regarding
perception, Friston basically posits that neural and cognitive systems are
engaged with trying to model the world they live in, and do so by looking for
models with maximum probability conditioned on the data they've observed.This is a useful but not adventurous
perceptive, and one can formulate it in terms of trying to find models
withminimum KL-divergence to reality,
which is one among many ways to describe Bayesian inference ... and which can
be mathematically viewed as attempting to minimize a certain "free
energy" function.

Friston then attempts to extend this
principle to action via a notion of "active inference", and this is
where things get dodgier. As the
above-linked "Markov Blankets" paper puts it,

"Active
inference is a cornerstone of the free energy principle. This principle states
that for organisms to maintain their integrity they must minimize variational
free energy. Variational free energy bounds
surprise because the former can be shown to be either greater than or equal to
the latter. It follows that any organism that minimizes free energy thereby
reduces surprise—which is the same as saying that such an organism maximizes
evidence for its own model, i.e. its own existence

...

This
interpretation means that changing internal states is equivalent to inferring
the most probable, hidden causes of sensory signals in terms of expectations
about states of the environment

...

[A]
biological system must possess a generative model with temporal depth, which,
in turn, implies that it can sample among different options and select the
option that has the greatest (expected) evidence or least (expected) free
energy. The options sampled from are intuitively probabilistic and future
oriented. Hence, living systems are able to ‘free’ themselves from their
proximal conditions by making inferences about probabilistic future states and
acting so as to minimize the expected surprise (i.e. uncertainty) associated
with those possible future states. This capacity connects biological qua
homeostatic systems with autonomy, as the latter denotes an organism’s capacity
to regulate its internal milieu in the face of an ever-changing environment.
This means that if a system is autonomous it must also be adaptive, where
adaptivity refers to an ability to operate differentially in certain
circumstances.

...

The
key difference between mere and adaptive active inference rests upon selecting
among different actions based upon deep (temporal) generative models that
minimize the free energy expected under different courses of action.

This
suggests that living systems can transcend their immediate present state and
work towards occupying states with a free energy minimum."

If you are a math/physics oriented person
and find the above quotes frustratingly vague, unfortunately you will find that
the rest of the paper is equally vague on the confusing points, and Friston's
other papers are also.

What it sounds like to me (doing some
"active inference" myself to try to understand what the paper is
trying to say) is that active inference is being portrayed as a process by
which cognitive systems take actions aimed at putting themselves in situations
that will be minimally surprising, i.e. in which they will have the most
accurate models of reality.If taken
literally this cannot be true, as it would predict that intelligent systems
systematically seek simpler situations they can model better -- which is
obviously not a full description of human motivation, for instance.We do have a motivation to put ourselves in
comprehensible, accurately model-able situations -- but we also have other
motivations, such as the desire to perceive novelty and to challenge ourselves,
which sometimes contradict our will to have a comprehensible environment.

The main thing that jumps out at me
when reading what Friston and colleagues write about active inference is that
it's too much about states and not enough about paths.To model far-from-equilibrium thermodynamics
using energy-based formalisms, one needs to think about paths and path
entropies and such, not just about things like " work[ing] towards occupying states with a free energy minimum."Instead of thinking about ideas like "selecting among different actions based
upon deep (temporal) generative models that minimize the free energy expected
under different courses of action." in terms of states with free
energyminimum, one needs to be thinking
about action selection in terms of stationarity of action functions evaluated
along multiple paths.

Energetics for Far-From-Equilibrium Thermodynamics

It seems clear that equilibrium
thermodynamics isn’t really what we want to use as a guide for cognitive
information processing.Fortunately, the
recent thermodynamics literature contains some quite interesting results
regarding path entropy in far-from-equilibrium thermodynamics.

The following table from Rogers and Rempe
summarizes some key points concisely.

Conceptually, the key point is that we need
to think not about the entropy of a state, but about the "caliber" of
a path -- a normalization of the number of ways that path can be realized.This then leads to the notion of the free
energy of a certain path.

It follows from this body of work that ideas
like "free energy minimization" need to be re-thought dynamically
rather than statically.One needs to
think about systems as following paths with differential probability based on
the corresponding path free energies.This is in line with the "Maximum
Caliber principle"which is a
generalization of the Maximum Entropy principle to dynamical systems (both
first proposed in clear form by E.T. Jaynes, though Maximum Entropy has been
more widely developed than Maximum Caliber so far).

Harking back to Friston for a moment, it
follows that the dynamics of an intelligent system, should be viewed, not as an
attempt by an intelligent system to find a state with minimum free energy or
surprisingness etc., but rather as a process of a system evolving dynamically
along paths chosen probabilistically to have stationary path free energy.

But of
course, this would be just as true for an unintelligent system as for an
intelligent system -- it's not a principle of intelligence but just a
restatement of how physics works (in far from equilibrium cases; in equilibrium
cases one can collapse paths to states).

If we want to say something unique about
intelligent systems in this context, we can look at the goals that an
intelligent system is trying to achieve.We may say that, along each potential path of the system's evolution,
its various goals will be achieved to a certain degree.The system then has can be viewed to have a
certain utility distribution across paths -- some paths are more desirable to
it than others.A guiding principle of
action selection would then be: To take an action A so that, conditioned on
action A, the predicted probability distribution across paths is as close as
possible to the distribution implied by the system's goals.

This principle of action selection can be
formalized as KL-divergence minimization if one wishes, and in that sense it
can be formulated as a "free energy minimization" principle.But it's a "free energy" defined
across ensembles of paths, not across states.

A side note is, it's important to understand
that the desirability of a path to an intelligent system need not be
expressible as the expected future utility at all moments of time along that
path.The desirability of a path may be
some more holistic function of everything that happens along that path.Considering only expected utility as a form
of goal leads to various pathologies related to wireheading, as I argued in a
long-ago blog post on ultimate orgasms and such.

Algorithmic Thermodynamics

Now let's dig a little deeper.Can we apply these same ideas beyond the
realm of physics, to more general types of processes that change over time?

I am inspired by a general Whiteheadean
notion of procesess as fundamental things.However, to keep things concrete, for now I'm going to provisionally
assume that the "processes" involved can be formulated as computer
programs, in some standard Turing-equivalent framework, or maybe a
quantum-computing framework.I think
the same ideas actually apply more broadly, but -- one step at a time...

Section 6 of Tadaki outlines a majorly aesthetic,
obvious-in-hindsight parallel between algorithmic information theory and
equilibrium thermodynamics.There is
seen to be a natural mapping between temperature in thermodynamics and
compression ratio in algorithmic information theory.A natural notion of "algorithmic free
energy"is formulated, as a sort of
weighted program-length over all possible computer programs (where the weights
depend on the temperature).

To ground the mappings he outlines,
Tadaki gives asimple statistical
mechanical interpretation to algorithmic information theory.He models an optimal computer as decoding
equipment at the receiving end of a noiseless binary communication
channel.In this context, he regards
programs for this computer as codewords (finite binary strings) and regards
computation results (also finite binary strings) as decoded “symbols.”For simplicity he assumes that the infinite
binary string sent through the channel -- constituting a series of codewords in
a prefix-free code is generated by infinitely repeated tosses of a fair
coin.Based on this simple reductive
model, Tadaki formulates computation-theoretic analogues to core constructs of
traditional equilibrium thermodynamics.

Now let's start putting some pieces together.

Perhaps the most useful observation I will
make in this blog post is:It
seems one could port the path-entropy based treatment of far-from-equilibrium
thermodynamics (as seen in the papers I've linked above) to Tadaki's
algorithmic-information context, by looking at sources emitting bits that are
not independent of each other but rather have some probabilistic dependencies..

By doing so, one would obtain an “algorithmic
energy” function that measures the energy of an algorithmic process over a
period of time -- without assuming that it’s a memoryless process like Tadaki
does in his paper.

To get this to work, so far as I can limn
without doing all the math (which I don't have time for at the moment, alas), one
needs to assume that the knowledge one has of the dependencies among the bits
produced by the process is given the form of expectations…e.g. that we know the average value of
f_k(x_{i+1}, x_i} for various observables f_k ….Plus one needs to make some other slightly
funny assumptions that are probably replaceable (the paper assumes “the number
of possible transitions does not depend on the starting point”… but I wonder if
this could be replaced by some assumption about causality…)

If I'm not mistaken, this should give us
something like Friston’s free energy principle that actually works and has
meaning….I.e. we have a rigorous sense
in which complex algorithmic systems are minimizing free energy.The catch is that it’s an algorithmic path
energy -- but hey...

More precisely, relative to an observer S who
is observing a system S1 in acertain
way (by tabulating conditional probabilities of “how often some event of type A
occurs at time T+s, given some event of type B occurred at time T”) … we may
say the evolution of S1 in S’s perspective obeys an energy minimization
principle, where energy is defined algorithmic-informationally (following my
proposed, not-yet-fleshed-out non-equilibrium generalization of Tadaki’s
approach)…

Into the Quantum Rabbit Hole...

Now that we've gone this far, we may as well
plunge in a bit deeper, right?

Tadaki deals w/ classical computers but --
gesticulating only moderately wildly -- it seems one could generalize his
approach to quantum computers OK.

Then one is looking at series of qubits
rather than bits, and instead of tabulating conditional probabilities one is
tabulating amplitudes.

The maximum entropy principle is replaced with
the stationary quantropy principle
and one still has the situation that: Relative to S who is observing S1 using
some standard linear quantum observables, S1 may be said to evolve according to
a stationary quantropy trajectory, where quantropy is here defined via
generalizing the non-equilibrium generalization of Tadaki’s
algorithmic-informational entropy via replacing the real values w/ complex
values

So we may well get a kind of free-energy
principle for quantum systems also.

If we want to model cognitive stuff using
bits or qubits, then we have here a physics-ish theory of cognitive
stuff….Or at least a sketch of the
start of one…

Out Toward the Eurycosm

One of the motivations for these
investigations was some discussions on higher-dimensional and more broadly
eurycosmic models of psi.If there are
non-physical dimensions that connect spatiotemporally distant entities, then
what are the dynamical laws in these dimensions?If we can model them as information
dimensions, then maybe the dynamics should be modeled as I’m alluding here…

Physics dynamics should be recoverable as a
special case of algorithmic-information dynamics where one adds special constraints.I.e. the constraints posed by spatial
structure and special relatively etc. should reflect themselves in the
conditional probabilities observed btw various classes of bits or qubits.

Then the linear symmetries of spacetime
structure should mean that when you calculate
maximum-path-algorithmic-information distributions relative to these physics
constraints, you end up getting maximum-Shannon-path-entropy
distributions.Because macrophysics
results from doing computing using ensembles of randomly chosen computer
programs (i.e. chosen subject to given constraints…).

Suppose we want to model a eurycosm that
works according to a principle like Peirce's "tendency to take
habits" aka
Smolin's Precedence Principle aka Sheldrake's morphic resonance?Well then, one can assume that the
probability distribution underlying the emanation of codewords in Tadaki's
model obeys this sort of principle.I.e., one can assume that the prior probability of a certain subsequence
is higher if that subsequence, or another subsequence with some of the same
patterns in that sequence, have occurred earlier in the overall sequence.Of course there are many ways to modify
Tadaki's precise computational model, and many ways to formalize the notion
that "subsequences with historically more frequent patterns should be more
frequent going forward."But
conceptually this is quite straightforward.

One is forced however to answer the following
question.Suppose we assume that the
probability of pattern P occurring in a subsequence beginning at time T is in
some way proportional to the intensity with which P has occurred as a pattern
in the subsequence prior to time T.What language of processes are we using to formalize the patterns
P?If -- in line with the framework I
articulate in The
Hidden Pattern and elsewhere -- we formalize a pattern P in X as a process
P that produces X and is simpler than X -- what is the language in which patterns
are expressed?What is the implicit programming language of
our corner of the eurycosm?

For simplicity I have been following Tadaki's conventional Turing machine based computational models here -- with a brief gesture toward quantum computing -- but of course the broad approach outlined here goes beyond these computing paradigms. What if we ported Tadaki's ideas to series of bits emanated by, say, a hypercomputer like the Zeno Machine? Then we don't just get a single infinite bit string as output, but a more complex ordinal construction with infinite bit strings of infinite bit strings etc. -- but the math could be worked. If the size of a Zeno Machine program can be quantified by a single real number, then one can assess Zeno Machine programs as patterns in data, and one can define concepts like compression ratio and algorithmic entropy and energy. The paradigm sketched here is not tied to a Turing Machine model of eurycosmic processes, though TMs are certainly easier for initial sketches and calculations than ZMs or even weirder things.

I have definitely raised more questions than
I've answered in this long and winding blog post.My goal has been to indicate a direction for
research and thinking, one that seems not a huge leap from the current state of
research in various fields, but perhaps dramatic in its utility and implications.

Sunday, July 14, 2019

One Basic Principle of this Corner of the Eurycosm: The Universe Maximizes Freedom Given Constraints of Reason and Beauty

I was musing a bit about the basic concept at the heart of quantum logic and quantum probability: That a particular observer, when reasoning about properties of a system that it cannot in principle ever observe, should use quantum logic / quantum probabilities instead of classical ones.

I kept wondering: Why should this be the case?

Then it hit me: It’s just the maximum-entropy principle on a higher level!

The universe tends to maximize entropy/uncertainty as best it can given the imposed constraints. And quantum amplitude (complex probability) distributions are in a way “more uncertain” than classical ones. So if the universe is maximizing entropy it should be using quantum probabilities wherever possible.

A little more formally, let’s assume that an observer should reason about their (observable or indirectly assessable) universe in a way that is:

logically consistent: the observations made at one place or time should be logically consistent with those made at other places and times

maximally entropic: having maximum uncertainty given other imposed constraints. Anything else is assuming more than necessary. This is basically an Occam’s Razor type assumption.

(I note that logical consistency is closely tied with the potential for useful abstraction. In an inconsistent perceived/modeled world, one can't generalize via the methodology of making a formal abstraction and then deriving implications of that formal abstraction for specific situations (because one can't trust the "deriving" part).... In procedural terms, if a process (specified in a certain language L) starting from a certain seed produces a certain result, then we need it still to be the case later and elsewhere that the same process from the same seed will generate the same result ... if that doesn't work then "pattern recognition" doesn't work so well.... So this sort of induction involving patterns expressed in a language L appears equivalent to logical consistency according to Curry-Howard type correspondences.)

To put the core point more philosophico-poetically, these three assumptions basically amount to declaring that an observer’s subjective universe should display the three properties of:

Reason

Beauty

Freedom

Who could argue with that?

How do reason, beauty and freedom lead to quantum logic?

I’m short on time as usual so I’m going to run through this pretty fast and loose. Obviously all this needs to be written out much more rigorously, and some hidden rocks may emerge. Let’s just pretend we’re discussing this over a beer and a joint with some jazz in the background…

We know basic quantum mechanics can be derived from a principle of stationary quantropy (complex valued entropy) [https://arxiv.org/abs/1311.0813], just as basic classical physics can be derived from a principle of stationary entropy …

It seems clear that modeling a system using complex truth values in a sense reflects MORE uncertainty than modeling a system using real truth values. What I mean is: The complex truth values allow system properties to have the same values they would if modeled w/ real truth values, but also additional values.

Think about the double-slit experiment: the quantum case allows the electrons to hit the same spots they would in the classical case, but also other spots.

On the whole, there will be greater logical entropy [https://arxiv.org/abs/1902.00741] for the quantum case than the classical case, i.e. the percentage of pairs of {property-value assignments for the system} that are considered different will be greater. Double-slit experiment is a clear example here as well.

So, suppose we had the meta-principle: When modeling any system’s properties, use an adequately symmetric information-theoretic formalism that A) maximizes uncertainty in one’s model of the system, B) will not, in any possible future reality, lead to logical contradictions with future observations.

By these principles — Reason, Beauty and Freedom — one finds that

for systems properties whose values cannot in principle be observed by you, you should use quantum logic, complex truth values, etc. in preference to regular probabilities (because these have greater uncertainty and there is no problematic contradiction here)

for system properties whose values CAN in principle be observed by you, you can’t use the complex truth values because in the possible realities where you observe the system state, you may come up with conclusions that would contradict some of the complex truth-value assignments

(E.g. in the double-slit experiment, in the cases where you can in principle observe the electron paths, the quantum assumptions can’t be used as they will lead to conclusions contradictory to observation…)

A pending question here is why not use quaternionic or octonionic truth values, which Youssef shows also display many of the pleasant symmetries needed to provide reasonable measure of probability and information. The answer has to be that these lack some basic symmetry properties we need to have a workable universe…. This seems plausibly true but needs more detailed elaboration…

So from the three meta-principles

logical consistency of our models of the world at various times

measurement of uncertainty according to a formalism obeying certain nice symmetry axioms

maximization of uncertainty in our models, subject to the constraints of our observation

we can derive the conclusion that quantum logic / complex probability should be used for those things an observer in principle can’t measure, whereas classical real probability should be used for those things they can…

That is, some key aspects our world seem to be derivable from the principle that: The Universe Maximizes Freedom Given Constraints of Reason and Beauty

What is the use of this train of thought?

I’m not sure yet. But it seems interesting to ground the peculiarity of quantum mechanics in something more fundamental.

The weird uncertainty of quantum mechanics may seem a bit less weird if one sees it as coming from a principle of assuming the maximum uncertainty one can, consistent with principles of consistency and symmetry.

Assuming the maximum uncertainty one can, is simply a matter of not assuming more than is necessary. Which seems extremely natural — even if some of its consequences, like quantum logic, can seem less than natural if (as evolution has primed us humans to do) you bring the wrong initial biases to thinking about them.

Tuesday, July 09, 2019

The "Simulation Hypothesis", the idea that our
universe is some sort of computer simulation, has been getting more and more
airtime lately.The rising popularity of the meme is not surprising
since virtual reality and associated tech have been steadily advancing, and at
the same time physicists have further advanced the formal parallels between
physics equations and computation theory.The notion of the universe as a computer simulation does
bring to the fore some important philosophical and scientific concepts that are
generally overlooked.However, in various online and real-world conversations I have been hearing various versions of the simulation hypothesis that don't make
a lot of sense from a scientific or rational point of view. So I wanted to write down briefly what does and doesn't make sense to me in the simulation-hypothesis vein...

One thing that has gotten on my nerves is hearing the simulation hypothesis used
to advocate for religious themes and concepts -- often in ways that profoundly stretch logic.There are some deep correspondences between the
insights of mystical wisdom traditions, and the lessons of modern physics and
computation theory -- but I have heard people talk about the simulation
hypothesis in ways that reach way beyond these correspondences, in a ways that fallaciously
makes it seem like the science and math give evidence for religious themes likethe existence of a vaguely anthropomorphic "creator" of our universe.This is, I suppose, what has led some
commentators like AGI researcher Eray Ozkural to label the simulation
hypothesis a new form of creationism (the link to his article "Simulation Argument and Existential AI Risk: New Age Creationism?" seems to be down at the moment).

The idea that our universe might be a computer simulation is
not a new one, and appeared in the science fiction literature many times
throughout the second half of the previous century.Oxford philosopher Nick Bostrom's essay titled
"The Simulation Argument" is generally credited with introducing
the idea to the modern science and technology community.Now Rizwan Virk's book titled
"The Simulation Hypothesis" is spreading the concept to an even
wider audience. Which is part of what motivated me to write a few words here on the topic.

I don't intend to review Virk's book here, because frankly I only skimmed it. It seems to cover a large variety of interesting topics related to the simulation hypothesis, and the bits and pieces I read were smoothly written and accurate enough.

Fundamentally, I think the Simulation Hypothesis as it's generally being discussed is not nearly crazy enough to be true. But it does dance around some interesting issues.

Bostrom's Rhetorical Trickery

I have considerable respect for Nick Bostrom's rhetorical
and analytical abilities, and I've worked with him briefly in the past when we
were both involved in the World Transhumanist Association, and when we
organized a conference on AI ethics together at his Future of Humanity
Institute.However, one issue I have
with some of Nick's work is his tendency to pull the high school debating-team
trick of arguing that something is POSSIBLE and then afterward speaking as if
he has proved this thing was LIKELY.He
did this in his book Superintelligence,
arguing for the possibility of superintelligent AI systems that annihilate
humanity or turn the universe into a vast mass of paperclips -- but then
afterward speaking as if he had argued such outcomes were reasonably likely or
even plausible.Similarly, in his
treatment of the simulation hypothesis, he makes a very clear argument as to
why we might well be living in a computer simulation -- but then projects a
tone of emphatic authority, making it seem to the naive reader like he has
somehow shown this isa reasonably
probable hypothesis.

Formally what Bostrom's essay argues is that

... at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation.

The basic argument goes like this: Our
universe has been around 14 billion years or so, and in that time-period a
number of alien civilizations have likely arisen in various star systems and
galaxies... and many of these civilizations have probably created advanced
technologies, including computer systems capable of hosting massive simulated
virtual-reality universes. (Formally, he argues something like this follows if we assume (1) and (2) are false.) So if we look
at the history of our universe, we have one base universe and maybe 100 or 1000
or 1000000 simulated universes created by prior alien civilizations.So what are the odds that we live in the
base universe rather than one of the simulations?Very low.Odds seem high that, unless (1) or (2) is true, we live in one of the simulations.

The obvious logical problem with this argument is: If we
live in a simulation programmed by some alien species, then the 14 billion year
history of our universe is FAKE, it's just part of that simulation ... so that
all reasoning based on this 14 billion year history is just reasoning about
what kind of preferences regarding fake evidence were possessed by the aliens
who programmed the simulation we're living in.So how do we reason about that?We need to place a probability distribution over the various possible
motivational systems and technological infrastructures of various alien
species?

(For a more detailed, slightly different run-through of this refutation of Bostrom's line of argument, see this essay from a Stanford University course).

Another way to look at it is: Formally, the problem with Bostrom's argument is that the confidence with which we can know the probability of (1) or (2) is very low if indeed we live in a simulation. Thus all his argument really shows is that we can't confidently know the probabilities of (1) and (2) are high -- because if we do know this, we can derive as a conclusion that the confidences with which we know these probabilities are low.

Bostrom's argument is essentially self-refuting: What it
demonstrates is mostly just that we have no frickin' idea about the
foundational nature of the universe we live in.Which is certainly true, but is not what he
claims to be demonstrating.

An Array of Speculative Hypotheses

To think seriously about the simulation hypothesis, we have
to clearly distinguish between a few different interesting, speculative ideas about the nature of our world.

One is the idea that our universe exists as a subset of some
larger space, which has different properties than our universe.So that the elementary particles that seem
to constitute the fundamental building-blocks of our physical universe, and the
3 dimensions of space and one dimension of time that seem to parametrize our
physical experience, are not the totality of existence -- but only one little corner
of some broader meta-cosmos.

Another is the idea that our universe exists as a subset of
some larger space, which has different properties than our universe, and in
which there is some sort of coherent, purposeful individual mind or society of
individual minds, who created our universe for some reason.

Another is that our universe has some close resemblance to part or all of the larger space that contains it, thus being in some sense a "simulation" of this greater containing space...

It is a valid philosophical point that any of these ideas
could turn out to be the reality.As
philosophy, one implication here is that maybe we shouldn't take our physical
universe quite as seriously as we generally do -- if it's just a tiny little
corner in a broader meta-cosmos.

One is reminded of the tiny little Who empire in Dr. Seuss's
kids' book "Horton Hears a Who."From the point of view of the Whos down there in Whoville, their lives
and buildings and such are very important.But from Horton the Elephant's view, they're just living in a tiny
little speck within a much bigger world.

From a science or engineering view, these ideas are only
really interesting if there's some way to gather data about the broader
meta-cosmos, or hack out of our limited universe into this broader meta-cosmos,
or something like that.This
possibility has been explored in endless science fiction stories, and also in
the movie The Matrix -- in which
there are not only anthropomorphic creators behind the simulated universe we
live in, but also fairly simple and emotionally satisfying ways of hacking out
of the simulation into the meta-world ... which ends up looking, surprise
surprise, a lot like our own simulated world.

The Matrix films also echo Christian themes in very
transparent ways -- the process of saving the lives and minds of everyone in
the simulation bottoms down to finding one savior, one Messiah type human, with
unique powers to bridge the gap between simulation and reality.This is good entertainment, partly because
it resonates so well with various of our historical and cultural tropes, but
it's a bit unfortunate when these themes leak out of the entertainment world
and into the arena of supposedly serious and thoughtful scientific and
philosophical discourse.

In a
2017 article, I put forth some of my own speculations about what sort of
broader space our physical universe might be embedded in.I called this broader space a Eurycosm
("eury" = wider), and attempted to explore what properties such a Eurycosm
might have in order to explain some of the more confusing aspects of our
physical and psychological universe, such as ESP, precognition, remote viewing
reincarnation, mediumistic seances, and so forth.I don't want to bog down this article with a
discussion of these phenomena, so I'll just point the reader who may be
interested to explore scientific evidence in this regard to a list ofreferences I posted some time ago.For
now, my point is just: If you believe that some of these "paranormal"
phenomena are sometimes real, then it's worth considering that they may be ways
to partially hack out of our conventional 4D physical universe into some sort
of broader containing space.

As it happens, my own speculations about what might happen
in a Eurycosm, a broader space in which our own physical universe is embedded,
have nothing to do with any creator or programmer "out there" who
programmed or designed our universe.I'm more interested to understand what kinds of information-theoretic
"laws" might govern dynamics in this sort of containing space.

What seems to be happening in many discussions I hear regarding the simulation hypothesis is: The realization that our 4D physical universe
might not be all there is to existence, that there might be some sort of
broader world beyond it, is getting all fuzzed up with the hypothesis that our
4D physical universe is somehow a "simulation" of something, and/or
that our universe is somehow created by some alien programmer in some other reality.

What is a "simulation" after all?Normally that word refers to an imitation of
something else, created to resemble that thing which it simulates.What is the evidence, or rational reason for
thinking, our universe is an imitation or approximation of something else?

Simulations like the ones we run in our computers today, are
built by human beings for specific purposes -- like exploring scientific
hypotheses, or making entertaining games.Again, what is the evidence, or rational reason for thinking, that there
is some programmer or creator or game designer underlying our universe?If the only evidence or reason is Bostrom's
argument about prior alien civilizations, then the answer is: Basically
nothing.

It's an emotionally appealing idea if you come from a
Christian background, clearly.And it's been funky idea for storytelling since basically the dawn of humanity, in one form or another.I told my
kids a bunch of simulation-hypothesis bedtime stories when they were young;
hopefully it didn't twist their minds too badly.My son Zebulon, when he was 14, wrote a novel
about a character on a mission to find the creators of the simulation we live
in, so as specifically to track down the graphic designer who had created the
simulation, so as to hold a gun to his head and force him to modify the
graphics behind our universe to make people less ugly.Later on he became a Sufi, a mystical
tradition which views the physical universe as insubstantial in much subtler
ways.

There is good mathematics and physics behind the notion that
our physical universe can be modeled as a sort of computer -- where the laws of
physics are a sort of "computer program" iterating our universe
through one step after the next.This
is not the only way to model our universe, but it seems a valid one that may be
useful for some purposes.

There is good philosophy behind the notion that our
apparently-so-solid physical reality is not necessarily foundationally real,
and may be just a tiny aspect of a broader reality.This is not a new point but it's a good
one.Plato's parable of the cave drove
this home to the Greeks long ago, and as Rizwan Virk notes these themes have a
long history in Indian and Chinese philosophy, and before that in various
shamanic traditions.Virk reviews some
of these predecessors in his book.

But there is nothing but funky entertainment and rampant
wishful thinking behind the idea that our universe is a simulation of some
other thing, or that there is some alien programmer or other vaguely
anthropomorphic "creator" behind the origin or maintenance of our
universe.

We Probably Have Very Little Idea What Is Going On

I have two dogs at home, and I often reflect on what they
think I am doing when I'm sitting at my computer typing.They think I'm sitting there, guarding some
of my valued objects and wiggling my fingers peculiarly.They have no idea that I'm controlling
computational processes on faraway compute clouds, or talking to colleagues
about mathematical and software structures.

Similarly, once we create AGI software 1000 times smarter
than we are, this software will understand aspects of the universe that are
opaque to our little human minds.Perhaps we will merge with this AGI software, and then the new
superintelligent versions of ourselves will understand these additional aspects
of the universe as well.Perhaps we
will then figure out how to hack out of our current 4D spacetime continuum into
some broader space.Perhaps at that
point, all of these concepts I'm discussing here will seem to my future-self
like absolute ridiculous nonsense.

I have a lot of respect for the limitations of human
intelligence, and a fairly strong confidence that we currently understand a
very minimal percentage of the overall universe.To the extent that discussion of the
simulation hypothesis points in this direction, it's possibly valuable and productive.We shouldn't be taking the 4D spacetime
continuum current physics models as somehow fundamentally real, we shouldn't be
assuming that it delimits reality in some ultimate and cosmic sense.

However, we also shouldn't be taking seriously the idea that
there is some guy, or girl, or alien, or society or whatever "out
there" who programmed a "simulation" in which our universe is
running.Yes, this is possible.A lot of things are possible.There is no reason to think this is decently
probable.

I can see that, for some people, the notion of a powerful
anthropomorphic creator is deeply reassuring.Freud understood this tendency fairly well -- there's an inner child in
all of us who would like there to be some big, reliable Daddy or Mommy responsible
for everything and able to take care of everything.Some bad things may happen, some good things
will happen, and in the end Mom and Dad understand more than we do and will
make sure it all comes out OK in the end.Nick Bostrom, for all his brilliance, seems repeatedly drawn to themes
of centralized control and wisdom.Wouldn't it be reassuring if, as he suggests in Superintelligence, the UN would take over the creation of AGI and
hire some elite vetted AI gurus to make sure it's developed in an appropriate
way?If we can't have a Christian God
watching over us and assuring us a glorious afterlife, can't we at least have
an alien programmer monitoring the simulation we're running in?Can't the alien programmer at least be really
good looking, let's say, maybe like a Hollywood movie star?

As far as I can tell, given my current sorely limited human
mind, the universe seems to be a lot more about open-ended
intelligence, a concept my friend Weaver at the Global Brain Institute has
expertly articulated.The universe --
both our 4D physical spacetime and whatever broader spaces exist beyond --
seems to be a complex, self-organizing system without any central purpose or
any centralized creator or controller.Think the creative self-organizing ocean in Lem's Solaris, rather than bug-eyed monsters coming down in spaceships to
enslave us or stick needles into our bellybuttons.

So the simulation hypothesis takes many forms. In its Bostromian form, or in the form I often hear it in casual conversations, it is mostly bullshit -- but still, it does
highlight some interesting issues.It's
a worthwhile thought experiment but in the end it's most valuable as a pointer
toward other, deeper ideas. The reality of our universe is almost surely way crazier than any story about simulations or creators, and almost surely way beyond our current imaginations.